Friction Causing Unpredictability

TL;DR

Adding friction to a simple double-well system introduces unpredictability in the final state due to complex basin structures, illustrating a route to chaos from initial uncertainties.

Contribution

The paper demonstrates how friction causes complex basin structures leading to unpredictability in simple systems, highlighting a new route to chaos.

Findings

Friction induces complex basin structures in phase space.

Finite initial uncertainty leads to unpredictable final states.

Friction can cause a transition from integrability to chaos.

Abstract

The periodic motion of a classical point particle in a one-dimensional double-well potential acquires a surprising degree of complexity if friction is added. Finite uncertainty in the initial state can make it impossible to predict in which of the two wells the particle will finally settle. For two models of friction, we exhibit the structure of the basins of attraction in phase space which causes the final-state sensitivity. Adding friction to an integrable system with more than one stable equilibrium emerges as a possible "route to chaos" whenever initial conditions can be specified with finite accuracy only.